An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at 12.7 m/s2 . at t1 the rocket engine is shut down and the sled moves with constant velocity v for another t2 s. the total distance traveled by the sled is 5.85 × 103 m and the total time is 94.6 s. find t1. answer in units of s.

The value of t₁ is 5.119 sec.

Explanation:

Given that,

Acceleration = 12.7 m/s²

Total distance

Time = 94.6 sec

We need to calculate the distance

Using equation of motion

Put the value into the formula

...(I)

We need to calculate the velocity

Using equation of motion

Put the value into the formula

The sled while moves with constant velocity v for time t₂

Using formula of distance

The total distance is

Put the value of s₁ and s₂

...(II)

The total time is

....(III)

From equation (II) and (III)

After solving

Hence, The value of t₁ is 5.119 sec.

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